Question

question 3 (1 point)
in the diagram, (mangle bda = 144^{circ}). find (mangle adc).
(7x + 34)° d (9x + 46)° a
o a 91°
o b 40°
o c 62°
o d 82°

Explanation:

Step1: Use angle - sum property

Since $\angle BDA+\angle ADC = 180^{\circ}$ (linear - pair of angles), and we know $m\angle BDA = 144^{\circ}$. Let $m\angle ADC=x$. Then $144^{\circ}+x = 180^{\circ}$.

Step2: Solve for $x$

Subtract $144^{\circ}$ from both sides of the equation: $x=180^{\circ}-144^{\circ}=36^{\circ}$. But we can also use the angle expressions. Since $\angle BDA=(7x + 34)^{\circ}+(9x + 46)^{\circ}=144^{\circ}$, first combine like - terms: $(7x+9x)+(34 + 46)=144$, which simplifies to $16x+80 = 144$.

Step3: Solve the equation for $x$

Subtract 80 from both sides: $16x=144 - 80=64$. Then divide both sides by 16: $x = 4$.

Step4: Find $m\angle ADC$

We know that $m\angle ADC=(9x + 46)^{\circ}$. Substitute $x = 4$ into the expression: $m\angle ADC=9\times4+46=36 + 46=82^{\circ}$.

Answer:

d. $82^{\circ}$